For regular research projects in Horizon 2020, Japanese partners are not eligible for automatic funding.
From the Horizon 2020 Japan Country page: As a high-tech country, well advanced in research and innovation, Japanese participants are, however, not automatically funded through Horizon 2020. Japanese participants have to determine themselves the sources of funding and find the resources for their part of the project. These may be own funds, as well as funds received from Japanese ministries, agencies, foundations and other organisations that fund research and innovation activities in Japan. (source: EC Website)
However, exceptionally they may be eligible for funding when the Commission deems participation of the entity essential for carrying out the action funded through Horizon 2020.
From the EC's explanation to evaluators: Part A of the General Annexes to the work programme includes the list of countries from which legal entities are automatically eligible for receiving funding from the Horizon 2020 budget. International European organisations are also eligible for funding. Unless otherwise stated in the work programme, legal entities from other countries and international organisations can only be funded in exceptional cases. One of those cases (Article 10.2.a of the Rules for Participation) is where the Commission deems the participation of the entity in question essential for carrying out the action. This exceptionality needs to be justified in the proposal and the Commission will base its decision on the evaluation of the proposal, which therefore needs to include the evaluators' judgment about whether or not the participation of the entity in question in the project is essential, with clear benefits to the consortium. These benefits may include, for example, outstanding competence and expertise, access to unique know-how, access to research infrastructures, access to geographical environments, involving key partners in emerging markets, access to data, etc. (source: EC Website)
There are also coordinated calls in Horizon 2020, in which Japanese participants will receive funding from the Japanese government, for example the joint ICT calls with MIC/NICT. Furthermore, in some calls support is given to Japanese participants through JST. In both cases, it is specifically written in the Horizon 2020 call text that this support is available. For current joint funding opportunities, please check our co-funding mechanisms page.
For individual researchers, Japanese researchers can participate in fellowship programmes in Europe and receive funding. Regarding ERC there is a specific arragement with JSPS for Japanese researchers to participate in ERC teams.